In what follows we will present our predictions for the prompt
atmospheric neutrino flux derived using the \(Z\) -moment method.
The effective hadronic interaction lengths \(\Lambda _i\)  and the \(Z_{pp}\) ,
\(Z_{HH}\)  and \(Z_{H\nu }\) -moments will be estimated following
Ref. [1]}.
On the other hand, the \(Z_{pH}\) -moment will be calculated using as
input the \(x_F\) -distribution for the charm production derived in
the hybrid approach with the ingredients discussed in the previous
section. Moreover, the prompt \(\nu _{\mu }\)  flux will be evaluated
considering the description of the primary
spectrum proposed by Gaisser in Ref. [2]}, denoted as
H3a spectrum, which assumes that it is given by a composition
of 3 populations and 5 representative nuclei, with the set of parameters
determined by a global fit of the cosmic ray data.
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